Quantum tunneling effect of a time-dependent inverted harmonic oscillator

Guo, Guangjie; Ren, Zhongzhou; Ju, Guo-Xing; Guo, Xiaoyong

doi:10.1088/1751-8113/44/18/185301

Cited by 15 publications

(26 citation statements)

References 37 publications

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“…k determines the barrier strength. The solutions of the Schrödinger equation for the time-dependent parabolic barrier can be obtained exactly by employing different methods, such as algebraic methods [7,8], dynamical invariant methods [9] or path-integral propagator methods [10]. These methods are usually transposed from the better known time-dependent harmonic oscillator problem (see [11] and references therein).…”

Section: Time-dependent Solutionsmentioning

confidence: 99%

“…Bob again repeats the earlier procedure for all particles, one by one, and in a way similar to the above is able to generate the curve T k (t ). Next, by comparing T f with T k , Bob is able to obtain t c , t d and hence, t , and then compute η using equations (8) and (9). The whole experiment is repeated by Alice and Bob many times for randomly chosen different values of the barrier strength k by Alice, leading to the inference in the above manner of the corresponding magnitude η(k) by Bob.…”

Section: Key Generation Scheme Using Early Arrivalsmentioning

confidence: 99%

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Effects of a transient barrier on wavepacket traversal

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Majumdar

Matzkin

2012

J. Phys. A: Math. Theor.

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An analytical treatment of a propagating wavepacket incident on a transient barrier reveals an effect in which, for a particular time interval, the timevarying transmission probability exceeds that for the free propagation of the wavepacket. We show that this effect can be interpreted semiclassically. This effect is quantified and it is shown that its magnitude is in one-to-one correspondence with the strength of the barrier, a feature that has the potential to be used in a scheme for key generation. It is found that the speed with which the information about the barrier perturbation propagates across the wavepacket can exceed the group velocity of the wavepacket. An application to the speed-up of entanglement generation is also considered.

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Section: Time-dependent Solutionsmentioning

confidence: 99%

Section: Key Generation Scheme Using Early Arrivalsmentioning

confidence: 99%

Effects of a transient barrier on wavepacket traversal

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Majumdar

Matzkin

2012

J. Phys. A: Math. Theor.

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“…As mentioned in [5], the term "inverted harmonic oscillator" (IO) originally refers to a model with negative kinetic and potential energy, as proposed in [6]. Nevertheless, most articles under the headline IO, actually consider the RO model, see, e.g., [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…It is then not anymore possible to construct coherent states by means of creation and annihilation operators; for a text book introduction see [10]. In [9], the RO was generalized by the assumption of a time-dependent mass and frequency. The corresponding Schrödinger equation was solved by means of an algebraic method with the aim to describe quantum tunneling.…”

Section: Introductionmentioning

confidence: 99%

Coherent States of Harmonic and Reversed Harmonic Oscillator

Rauh

2016

Symmetry

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A one-dimensional wave function is assumed whose logarithm is a quadratic form in the configuration variable with time-dependent coefficients. This trial function allows for general time-dependent solutions both of the harmonic oscillator (HO) and the reversed harmonic oscillator (RO). For the HO, apart from the standard coherent states, a further class of solutions is derived with a time-dependent width parameter. The width of the corresponding probability density fluctuates, or "breathes" periodically with the oscillator frequency. In the case of the RO, one also obtains normalized wave packets which, however, show diffusion through exponential broadening with time. At the initial time, the integration constants give rise to complete sets of coherent states in the three cases considered. The results are applicable to the quantum mechanics of the Kepler-Coulomb problem when transformed to the model of a four-dimensional harmonic oscillator with a constraint. In the classical limit, as was shown recently, the wave packets of the RO basis generate the hyperbolic Kepler orbits, and, by means of analytic continuation, the elliptic orbits are also obtained quantum mechanically.

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“…What role this instability effects does play? Examples of application of non-autonomous Hamiltonian systems can be found in a huge range of areas of physics, in particular: in quantum optics, where a harmonic oscillator with time dependent frequency is shown to generate squeezing [11,12], tunneling [13], exact solutions for mathematical problems and toy models [14], parametric amplification [15], quantum Brownian motion [16]. Most of these works employs the model of the harmonic oscillator with time dependent frequency.…”

Section: Introductionmentioning

confidence: 99%

Parametric competition in non-autonomous Hamiltonian systems

Souza

Faria

Nemes

2014

Optics Communications

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In this work we use the formalism of chord functions (i.e. characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial state. We analytically obtain a solution for the characteristic function under dissipation, and therefore for the determinant of the covariance matrix and the von Neumann entropy, where the latter is the physical quantity of interest. We study in details two examples that are known to show dynamical squeezing and instability effects: the inverted harmonic oscillator and an oscillator with time dependent frequency. We show that it will appear in both cases a clear competition between instability and dissipation. If the dissipation is small when compared to the instability, the squeezing generation is dominant and one can see an increasing in the von Neumann entropy. When the dissipation is large enough, the dynamical squeezing generation in one of the quadratures is retained, thence the growth in the von Neumann entropy is contained.

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Quantum tunneling effect of a time-dependent inverted harmonic oscillator

Cited by 15 publications

References 37 publications

Effects of a transient barrier on wavepacket traversal

Effects of a transient barrier on wavepacket traversal

Coherent States of Harmonic and Reversed Harmonic Oscillator

Parametric competition in non-autonomous Hamiltonian systems

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